A292234 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals eight.

1, 2, 7, 23, 78, 262, 893, 3039, 10405, 35692, 122807, 423392, 1462748, 5061942, 17544791, 60893535, 211610421, 736189821, 2563823467, 8937012397, 31179543205, 108865543805, 380389514123, 1330027798273, 4653356214277, 16290208735442, 57059113819218

Offset

8,2

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Index entries for sequences related to rooted trees

Maple

b:= proc(n, i, v, k) option remember; `if`(n=0,
      `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
      `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
       b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
    end:
A:= proc(n, k) option remember; `if`(n<2, n,
      add(b(n, n+1-j, j, k), j=2..min(n, k)))
    end:
a:= n-> A(n, 8)-A(n, 7):
seq(a(n), n=8..35);

Crossrefs

Column k=8 of A292086.

Sequence in context: A292231 A292232 A292233 * A292235 A292236 A292087

Adjacent sequences: A292231 A292232 A292233 * A292235 A292236 A292237

Keyword

nonn

Author

Alois P. Heinz, Sep 12 2017

Status

approved